Differentiate the function y = cot(4x).

The derivative of y = cot(4x) is -4csc²(4x).

To differentiate y = cot(4x), we need to use the chain rule. Let u = 4x, then y = cot(u). Using the chain rule, we have:

dy/dx = dy/du * du/dx

To find dy/du, we use the derivative of cot(u), which is -csc²(u). Substituting back in for u, we have:

dy/du = -csc²(4x)

To find du/dx, we simply take the derivative of u with respect to x, which is 4. Substituting both values back into the chain rule equation, we have:

dy/dx = -csc²(4x) * 4

Simplifying, we get:

dy/dx = -4csc²(4x)

Therefore, the derivative of y = cot(4x) is -4csc²(4x).